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Physical Review A

Generation and properties of collective atomic Schrödinger-cat states

Christopher C. Gerry, R. Grobe

Published Sep 1, 1997• 56 citations
Publisher

Abstract

We propose a method for generating collective atomic Schr\"odinger-cat states formed as superpositions of the Bloch (or atomic coherent) states in the context of cavity QED. We then study the properties of these states and show the effects of the superpositions on spontaneous and stimulated emission, the atomic dipole moment, spin squeezing, and coherence.

DOI
10.1103/physreva.56.2390

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We propose a method for generating collective atomic Schr"odinger-cat states formed as superpositions of the Bloch (or atomic coherent) states in the context of cavity QED. We then study the properties of these states and show the effects of the superpositions on spontaneous and stimulated emission, the atomic dipole moment, spin squeezing, and coherence.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
Higher-generation Schrödinger cat states of the quantized electromagnetic field can be produced in a high-Q cavity, starting from a coherent state, through the passage of prepared Rydberg atoms interacting dispersively across it. These states are natural generalizations of the even and odd coherent states, the N th-generations corresponding to specific superpositions of 2 N states on a circle in phase space with well defined parity, and present very peculiar properties. Their photon statistics interchange between super- and sub-Poissonian behaviours and the nature of the photon bunching oscillates as the field intensity in the cavity is varied. For higher-generation even states, the minimum value of the Mandel factor almost reaches −1.0 and the state represents the Fock state |2 N ). Squeezing properties and the Wigner function of these higher-generation Schrödinger cat states are also considered.
We propose an alternative scheme for generation of atomic Schrödinger cat states in an optical cavity. In the scheme the atoms are always populated in the two ground states and the cavity remains in the vacuum state. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay. The scheme may be generalized to the deterministic generation of entangled coherent states for two atomic samples. In contrast with the previously proposed schemes of [Commun. Theor. Phys. 40 (2003) 103 and Chin. Phys. B 18 (2009) 1045], the required interaction time in our scheme is greatly shortened and thus the decoherence can be effectively suppressed.